The subject of matrix theory can be regarded as a bridge between the abstract structures of mathematics, and their engineering applications. Definitions, and elementary properties of matrices and determinants are briefly discussed in this chapter. Matrices as examples of linear mappings or transformations (operators) are also explored. Spectral analysis of matrices, Hermitian matrices and their eigenstructures, Perron-Frobenius theory of positive and nonnegative matrices, singular value decomposition, matrix calculus, and random matrices are also studied.